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Find the values of m such that the line does not touch the parabola

  1. Mar 6, 2012 #1
    1. The problem statement, all variables and given/known data

    for what values of m does the line with equation y = mx - 12 not intersect or touch the parabola with equation y = 2x^2-x-10. Please show working out & explain.

    2. Relevant equations



    3. The attempt at a solution

    This question was asked on openstudy and there hasn't been an answer to it yet. It's been 5 years since I've taking algebra and pre-calc, so there's certain things I don't remember how to do such as this question.

    Would anyone know how to approach this? I'm just extremely curious :-)
     
  2. jcsd
  3. Mar 6, 2012 #2

    HallsofIvy

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    Staff Emeritus
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    At a point, (x,y), where the two graphs intersect, the x and y values must be the same- that is, there exist a value of x such that [itex]y= 2x^2- x- 10= mx- 12[/itex]. That's a quadratic equation, it reduces to [itex]2x^2- (1-m)x+ 2= 0[/itex], and so has either 2 real roots (the line crosses the parabola), 1 double root (the line is tangent to the parabola), of no real roots (the line does not touch the parabola). Use the quadratic formula to determine what m must be so that equation has no real roots.
     
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